A368487 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^j * binomial(j+k-1,j).

1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 10, 17, 4, 1, 1, 17, 64, 49, 5, 1, 1, 26, 177, 334, 129, 6, 1, 1, 37, 401, 1457, 1549, 321, 7, 1, 1, 50, 793, 4776, 10417, 6652, 769, 8, 1, 1, 65, 1422, 12889, 48526, 67761, 27064, 1793, 9, 1, 1, 82, 2369, 30234, 176185, 442276, 411825, 105796, 4097, 10, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

G.f. of column k: 1/((1-x) * (1-k*x)^k).

Example

Square array begins:
  1, 1,   1,    1,     1,      1, ...
  1, 2,   5,   10,    17,     26, ...
  1, 3,  17,   64,   177,    401, ...
  1, 4,  49,  334,  1457,   4776, ...
  1, 5, 129, 1549, 10417,  48526, ...
  1, 6, 321, 6652, 67761, 442276, ...

Prog

(PARI) T(n, k) = sum(j=0, n, k^j*binomial(j+k-1, j));

Crossrefs

Columns k=0..3 give A000012, A000027(n+1), A000337(n+1), A367591.

Main diagonal gives A368488.

Cf. A119258, A368486.

Sequence in context: A079213 A047884 A124328 * A055818 A106240 A340561

Adjacent sequences: A368484 A368485 A368486 * A368488 A368489 A368490

Keyword

nonn,tabl,easy

Author

Seiichi Manyama, Dec 26 2023

Status

approved